College Calculus: Level II Ratio Test and Root Test

In this video we are going to talk about the Ratio Test and the Root Test. So, first, we are going to talk about some important definitions and theorems. There are three classifications that we are going to be using for series from now on. First one is absolutely convergent, second one is conditionally convergent and third is divergent. We are going to talk about possibility that one case is missing from these three categories and see why that cannot happen. We have two tests to help us determine which case we actually have. Those are Ratio Test and Root Test. We will do some examples to see how this works.

Here are some flags that might suggest that you not use the Ratio Test:

n, n² (or any polynomial), √n, ln n. All of these have lim = 1, so the Ratio Test fails. But if you have some of this clutter mixed with some good stuff, Ratio is great for clearing the clutter away and leaving you with something good.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Ratio Test and Root Test

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.